Francis Bonahon - Cyclic representations of the quantum coordinate ring O_q(SL_2) - IPAM at UCLA
Recorded 13 October 2026. Francis Bonahon of Michigan State University presents "Cyclic representations of the quantum coordinate ring O_q(SL_2)" at IPAM's Hyperbolic Structures and Quantum Invariants Workshop.Abstract: Many of the original quantum invariants are based on representations of the quantum group U_q(sl_2) or, more or less equivalently, corepresentations or its Hopf dual O_q(SL_2). Whereas U_q(sl_2) is a deformation of the enveloping algebra of the Lie algebra sl_2, its dual O_q(SL_2) is a deformation of the algebra of functions on the Lie group SL_2. It turns out that, when the quantum parameter q is a root of unity, O_q(SL_2) also has interesting representations. I will discuss several features of the corresponding representation category, and in particular how it is closely connected to the geometry of the Lie group SL_2.
This is joint work with Matt Harper.
Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-i-hyperbolic-structures-and-quantum-invariants/?tab=overview Receive SMS online on sms24.me
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